$$ax+by=c$$
$\left\{\begin{matrix}a=-\frac{by-c}{x}\text{, }&x\neq 0\\a\in \mathrm{C}\text{, }&c=by\text{ and }x=0\end{matrix}\right.$
$\left\{\begin{matrix}b=-\frac{ax-c}{y}\text{, }&y\neq 0\\b\in \mathrm{C}\text{, }&c=ax\text{ and }y=0\end{matrix}\right.$
$\left\{\begin{matrix}a=-\frac{by-c}{x}\text{, }&x\neq 0\\a\in \mathrm{R}\text{, }&c=by\text{ and }x=0\end{matrix}\right.$
$\left\{\begin{matrix}b=-\frac{ax-c}{y}\text{, }&y\neq 0\\b\in \mathrm{R}\text{, }&c=ax\text{ and }y=0\end{matrix}\right.$